Carl Herrmann

Phil Sidney Ostheimer, Mayank Nagda, Andriy Balinskyy et al.

Diffusion models (DMs) excel on dense continuous data, but are not designed for sparse continuous data. They do not model exact zeros that represent the deliberate absence of a signal. As a result, they erase sparsity patterns and perform unnecessary computation on mostly zero entries. With Sparsity-Exploiting Diffusion (SED), we model only non-zero values, preserving sparsity. SED delivers computational savings while maintaining or improving generation quality by skipping zeros during training and inference. Across physics and biology benchmarks, SED matches or surpasses conventional DMs and domain-specific baselines, while vision experiments provide intuitive insights into the limitations of dense DMs and the benefits of SED.

Phil Ostheimer, Mayank Nagda, Jean Radig et al.

Sparse data is ubiquitous, appearing in numerous domains, from economics and recommender systems to astronomy and biomedical sciences. However, efficiently generating high-fidelity synthetic sparse data remains a significant challenge. We introduce Sparse Data Diffusion (SDD), a novel method for generating sparse data. SDD extends continuous state-space diffusion models with an explicit representation of exact zeros by modeling sparsity through the introduction of Sparsity Bits. Empirical validation in various domains, including two scientific applications in physics and biology, demonstrates that SDD achieves high fidelity in representing data sparsity while preserving the quality of the generated data.